


GEN 0 particles, or “too OCD”

by Charles_Rockafellor



Category: Meta - Fandom
Genre: Alternative QCD, Alternative QED, Atomic nuclei, Extrapolation, Gluons, Hadrons, Leptons, Nuclear fusion, Quarks, particle physics
Language: English
Status: Completed
Published: 2021-02-28
Updated: 2021-02-28
Packaged: 2021-03-15 19:13:41
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 8,037
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/29688639
Author URL: https://archiveofourown.org/users/Charles_Rockafellor/pseuds/Charles_Rockafellor
Summary: In the previous meta piece, we looked at real world hadrons with an eye toward building story-worlds for hardcore sci-fi.  Here we look at an example of changing things – the “What if?” scenario; specifically: the collapse of a false vacuum to a lower energy state consistent withzeroeth-generation quarks.  This meta piece examines how things might change (or be required to be different in the first place) if such were to come about in the world as we currently know it.Why?Because it gives us a look at how one might go about pursuing such differences more rigorously than by using the soft-core funsies method.
Collections: Worldbuilding Meta





	GEN 0 particles, or “too OCD”

**Author's Note:**

> I haven't actively incorporated the GEN 0 leptons, quarks, and hadrons into any fics (beyond their glancing mention in Sonic's chapter-2-[flashback](https://archiveofourown.org/works/24230851/chapters/58380841), where we caught only a glimpse of a world-ending transformation), but I had an idea in 3Q20 that I'm still thinking about (working title is “An action of the peace”): an ST:TOS/TNG [mix] crossover from SG:A (possibly with WH40K chaos warp coming into play), the underlying details having been inspired by Asimov's 186Pu in “[The gods themselves](https://en.wikipedia.org/wiki/The_Gods_Themselves)”.
> 
> Also: the data that I used when I wrote this up in 2018 are probably slightly different by now. If you want the most up to date info (e.g.: [2020 PDG](https://pdg.lbl.gov/2020/listings/contents_listings.html)), then these are close, but no cigar. OTOH, one sometimes needs period-info rather than the most current info, so if you were to write a fic from the POV of '40s pulp sci-fi (ahh, the golden age!), then you might want to use '40s data as your starting points and extrapolate what _they'd_ expect such particles to be like (or rather, since they had no knowledge of higher-generation quark models: what such lower-generation particles might be like in accordance with the particle data of the '40s).
> 
> For further meta reading, see also (hadrons and superpowers are already linked on AO3 below, logic is still in Notes on Facebook so far [but coming soon to AO3]):
> 
>   * “[The Hadron Octahedron](https://archiveofourown.org/works/29512119)”, 
>   * “[Superheroes: Powers and Principalities](https://archiveofourown.org/works/29371374)”, 
>   * and “[The Categorical Logic Cube](https://www.facebook.com/notes/charles-rockafellor/the-categorical-logic-cube/3133287730034880/)”. 
> 


  
**Contents:**  
[Intro]  
Masses  
Nuclei and chemistry  
Terrestrial conditions  
Stellar fusion  
Quark stars  
Solar evolution  
Element distribution  
Conclusion  
Addendum  


#### Zeroeth generation quarks: a flight of fancy

I don't know if anyone's looked into a further spontaneous symmetry breaking of forces (e.g.: X ~1028 eV [≈1032 K] → G+ES ~1025 eV [≈1029 K] → G+S+EW ~1011 eV [≈1015 K] → G+S+W+EM → {G+S+W+E+M or G+S+W+EM+W'}), and if so then they probably found it to be completely meaningless garbage, unless you count the possibility of false vacuum decay. The same goes for further particle decoupling or particle generations in extremely low energy regimes (current record: 5*10-8 K ≈ 4.309(-)*10-12 eV [far below even quantum computer temperatures], which we can reach without suddenly seeing strange new ultralight-weight particles condense out of the vacuum – but hey, maybe such a transition would hinge upon a combination of energy density _and_ minimum n-volume [though I'm not aware of such having obtained in previous cases]); something similar with false vacuum decay seems to have been considered by Coleman and De Luccia (“ _[Gravitational effects on and of vacuum decay](http://www.sns.ias.edu/pitp2/2011files/PhysRevD.21.3305.pdf)_ ”, Phys. Rev. D, vol. 21, no. 12, 15 Jun 1980), with the result being an anti-de Sitter space decaying within microseconds.

Maybe we'd need to “freeze” space in the middle of a Big Rip (at some point _prior to_ a phantom-driven quark-antiquark pair production overdrive [assuming that the jerk or snap rates don't cause comoving space's expansion rate to exceed force-carrying causality speed – though if so, then what would a Rip do to point-particles?], much less singularity). (Why not? We can now freeze light in a B.E.C. – an utterly _preposterous_ proposition on the surface, not many years ago.) Alternatively, if one had a compactified dimension that expanded accordion-like to some extent without affecting the macroscale dimensions, then the overall energy density would drop without having “gone” anywhere (assuming that the vacuum energy didn't scale with the n-volume). Mind you, this paragraph goes off rather farther into Cloud Cuckoo Land than I really wish to entertain, and my purpose for this write-up isn't the “ _how might_ ” so much as the “ _and consequently_ ”.

So: **_what if_**...? (For that matter, what might the universe be like if GEN 2 became the end of the line, with no GEN 1, or if any of the masses [and/or other properties] were adjusted to someplace along the scale other than where they are? If one were to induce such a state of affairs for the universe as a whole, and stand back and watch the fireworks from some god-like perspective, then I suppose that the then-impossible GEN 1 particles would have to either spontaneously merge into then-stable GEN 2s or perhaps dissipate in a puff of uncertainty into photons and neutrinos [sort of as if they were virtual particle pairs].)

What I sought to describe with Sonic's memory of Cherenkov radiation and plasmons and a supercooled pond was a single, protracted instant of phase transition happening at random points just before something like a chaotic inflation of the Z.P.E. being dropped to a new low at _all_ points, like nucleating bubbles of steam that haven't quite yet coalesced to an explosion of combined surface area (it makes me think of Q-switching, but I can't quite put my finger on just why). That doesn't convey the picture accurately at all, but hopefully it mixes the imagery in a way that carries the feeling aptly. Picture something like a plane-fronted gravitational wave bursting outward; imagine applying that to a special case wherein our universe were DIM 2 and the front were a manifold impinging from without, giving an expanding circular domain wall around the disc of intersection – now make that wave front sponge-like in its topology (or at least in its topographic contours relative to the universal plane), and the result isn't a single point that expands from some origin, but rather more like the DIM 2 cross section of five fingers expanding as they intersect with the plane even though they're all part of a single hand (and not necessarily all at the same rates, since the contour tangents might be variable): basically a non-local Rayleigh-Taylor instability of a sort, more like collision with a cylindrical hairbrush fiber bundle than with a p-brane (I keep picturing it as sort of a quiver diagram of _possible_ pilot waves condensing to _reified_ fracture lines – that's not a very scientific picture, so I'll have to see if I can edit this later to something more accurate; the other metaphor in mind is even less realistic: a compass flip-flopping between two entirely different “north” poles). Sonic's incomplete memory of that event left open the question of whether the inflating regions eventually merged continuously vs. leaving irregularities (such as monopolar, cosmic string, and domain wall equivalents).

If you've read and enjoyed Abbott's “ _Flatland_ ” or Dewdney's “ _Planiverse_ ”, then you might have had the let's-have-some-fun bug grab you at some point – so let's see what we can do with the idea of GEN 0 particles. It'll be **_a toy model_** , but it could still be fun.

To be clear, though: I'm not a physicist. I've had some calculus, done some self-study, etc., but am not particularly qualified in wave functions or equations of state.

#### GEN 0 masses **Contents ▲**

Assuming that such a further phase transition were possible, then perhaps we'd see quarks (and/or other particles) decohere into lighter modes. I've no idea what they could be like by any current research, so let's just have some fun with spitballing it (I'll work with [PDG's data as of 18 Mar 2019](http://pdg.lbl.gov/2018/listings/contents_listings.html) [data date-cutoff = 15 Jan 2018 {the 2018 PDG sheets mention the CODATA 2010 value, but their comments seem to indicate that the CODATA 2014 value was used; the e- and µ- masses in MeV match the CODATA 2014 value through 9 decimal places}], to include their GEN 4 highest-value mass-minima shown for reference):

  
**_[open image in new tab](https://i.pinimg.com/originals/f0/cb/22/f0cb225e7a39922c1ca0963d77f88e4b.png) to zoom_**

Note that the u0 remains less massive than the d0 and is presumably more stable, much as with their GEN 1 original counterparts. N.B.: these GEN 0 numbers were extrapolated _without_ the evidential lower limits of [GEN 4] b' and t'. Also: yes, neutrinos used to be thought to be massless, but have since the late '90s seemed to be of non-zero mass, so I've included their 2018 PDG experimental upper limits for reference; these estimates aren't exactly the same as the old KamLAND mass-eigenstate oscillation squared-mass estimates, or masses deduced from galactic lensing extrapolations, but at least they're all from the same source as the quarks' data, so I'll call it good enough for now.

Now, these look O.K.-enough _here_ , and the spreadsheet-snapshot (next figure down) shows how I arrived at these values for GEN 0 (though I still look at the flip-flop in charge-mass distribution [↑u<↓d, ↑c>↓s, ↑t>↓b {arrows here not intended to indicate spin}] as being “funny”, but weird little quirks make things interesting); it's only a naïve model, meant to extend things enough to work with.

  
**_[open image in new tab](https://i.pinimg.com/originals/74/94/1a/74941ae0d1a8d29e13d12ca2ac5780b9.png) to zoom_**

  
**_[open image in new tab](https://i.pinimg.com/originals/a8/05/f2/a805f21a1fa0bcecc1119a4d7bfae3a8.png) to zoom_**

Why these values for GEN 0? I don't have a good, solid, scientific reason for them: I simply looked at the rate of change between each _known_ generation's masses, and those changes' rates of change, and applied that to the GEN 1 particles for a shits-and-giggles regression. A sound enough _starting_ point, but I'd be astounded if these results were even remotely like those of a rigorous analysis (particularly since the masses are well above the lowest temperatures that we've so far delved to in practice – then again, liquid water solidifies to ice at low temperatures, rather than breaking down into component ions or hadrons and leptons, and can supercool without necessarily freezing, so maybe not having seen GEN 0 particles as yet doesn't mean much, and we'll encounter a [real or hypothetical] GEN 1→0 explosive decompression at some point [I can see it now: something like a neutron star evaporating enough mass to begin boiling off its neutrons as protons, electrons, and antineutrinos]). For the purpose of extrapolating GEN 0 particles' populations and properties in a fanfic's tangent's irrelevant-appendix (originally), even this is probably more than good enough (I'm already counting how many pins are dancing on the head of an angel, or something like that).

I tried some other quick extrapolations; most were much worse (I don't mean simply that they gave GEN 0 and 4 numbers that I didn't like, I mean that they just didn't fit even the known GEN 1-3 data very well). Below are examples for the up-type and down-type quarks, electron-type leptons, and neutrino-type leptons in the polynomial regression; I'll skip all but the up-type quarks in the other trends, since the point is only that all of these fit the known masses less well than the naïve approach that I used earlier:

Polynomial regression  
y = 85231.125 x2  
– 254425.625 x  
\+ 169196.75  
⸫ GEN 0↑ = 169196.75 [far too heavy];  
GEN 4↑ = 515192.25 [too light]  
y = 1996.9 x2  
– 5897.5 x  
\+ 3905.4  
⸫ GEN 0↓ = 3905.4 [too heavy];  
GEN 4↓ = 12265.8 [too light]  
y = 783.077125 x2  
– 2244.083999 x  
\+ 1461.517873  
⸫ GEN 0 ℓ± = 1461.517873 [too heavy];  
GEN 4 ℓ± = 5014.415877 [too light]  
y = 8.910001 x2  
– 26.540005 x  
\+ 17.630006  
⸫ GEN 0 v0 = 17.630006 [far too heavy];  
GEN 4 v0 = 160.190022 [unk.]

Linear trend  
f(x) = 86498.875 x  
– 114907  
⸫ GEN 0↑ = 2090.1 x  
– 2750.93̅  
GIGO

Logarithmic trend  
f(x) = 140709.667145553 ln(x)  
– 25948.5428399908;  
⸫ GEN 0↑ = 3409.7326426177 ln(x)  
– 607.2069166487  
GIGO

Exponential trend  
f(x) = 0.0102836478  
exp(5.6250583286 x)  
⸫ GEN 0↑ = 0.1437474117  
exp(3.3853230325 x)  
GIGO

Power trend  
f(x) = 1.8730836914  
x^10.1218892736  
⸫ GEN 0↑ = 3.5488336011  
x^5.9678704669  
GIGO

If a nonzero portion of GEN 1 quarks' mass in that scenario were to come from stabilizing them against decaying to GEN 0 states, then the total population of GEN 0 would be less than the simple division of GEN 1; that is, presumably GEN 1 up-quark decay channels would display the largest branches via some virtual-W path into _far fewer than_ the maximum possible [by mass] of ~2,339 GEN 0 up-type-quarks in this model (probably just one of them, actually, with the remaining mass-energy mostly being bound up as a GEN 0 lepton and a GEN 0 antineutrino [or vice versa], or as a GEN 0 meson) - except that weak decay would require the GEN 1 up-type to switch to down-type upon decay to GEN 0, and vice versa, of course.

When GEN 2 quarks decay, they generally don't turn into cascades of GEN 1 quarks; they _usually_ (branching ratio / branching fraction) turn into just the one (a weak-induced electrical-charge-swap and typically becoming the next-most-massive quark [aside from the usual weirdness of d-vs.-u]) with a little something extra here and there _sometimes_ , and the rest of their GEN 2 mass-energy presents now as momentum and such. The same holds for GEN 3 quarks. I'm going to assume here that the same again would hold for GEN 1→0 decay paths: instead of the common image that's something like an atomic nucleus shattering into a zillion component pieces like a lego toy that's been dropped onto the floor, picture spinning your arm fast so that the **_single_** stem of a dandelion (like some lower GEN n-1 quark) left a few puffy bits behind it (the decay's results' released energy being represented as the stem's velocity); maybe soap bubbles would be more apt.

GEN 1→0 hadron decay would presumably exhibit some sort of conservation constraint(s), as seen in EM charge conjugation of π0 (e.g.: π0 → γ charge and momentum violation, or π0 → γ + γ + γ charge violation only), or the GEN 2→1 strangeness conservation of Λ0 (giving us a GEN 1→0 weak decay something like {p+ →W- **_p_** +0 \+ **_π_** 00} **::** {ud ** _d_** →W- **_u_** 0ud + **_u̅_** 0 ** _d_** 0}).

Note that such a transition on its own shouldn't directly affect anything else; e.g.: while it might mean a higher background radiation level (e.g.: Earth, if it somehow survived, would be bathed in ~99.94(+)% of its mass [simply assuming a mean average of quarks' and leptons' GEN 1:0 mass ratios] in the form of GEN 0 leptons, neutrinos, and mesons [presumably triggering secondary cascades] until it radiated away, and ignoring all of the other resultant radiation in the universe and the resultant long-term issue of its orbit being too large for the leftover sun's ~0.06(-)% mass to retain the leftover planet [though this might take a little while before being a problem, since only the surface of the sun would lose mass immediately, as the non-neutrino results wound their way around in an attempt to escape], if the sun somehow also survived such a transition) and a lower mass-density of interstellar medium (~0.06(-)% of current mass [or ~0.05(+)% if we assume all-hydrogen], hence less drag for a spaceship, for example), it shouldn't also increase [for example] the speed of light in vacuo (unless such a transition [consequently or coincidentally] also reduced electric permittivity [ε0] and/or magnetic permeability [µ0] of free space appropriately [and/or introduced some third-or-more fractional term(s)], which would necessarily increase the speed of light in vacuo).

What would all of that amount to in simple terms? I can't guarantee this, but I'm pretty sure that we'd be dead. By definition here, GEN 1 quarks are assumed to be fairly unstable in contrast to GEN 0 (though GEN 1 hadrons might be longer-lived there than GEN 2 hadrons are here – maybe you could even have GEN 1 stars showing up in a specific mass range [just as glasma / QGP stars _might_ here, though I suspect that the equivalent there would likely be a mixed state GEN 0+1 star], with “weird” GEN 1 chemistry). My **first** thought **was** that (since quark masses dropped a mean average of ~2 magnitudes and lepton mass dropped ~4) GEN 0 atoms [e.g.: H00] would have very tight e-0 orbitals (possibly remaining within the nucleus [though we'll see in a few paragraphs that my guess gives a velocity _uncertainty_ >c]), given their minuscule mass in ratio to p+0 (and I'm not so sure that n00 would be terribly stable). There might be some chemistry that life could evolve from, maybe even far more easily and interestingly than with GEN 1 baryons (much as we imagine wholly- and partly-strange nuclei today, a GEN 0 world might very well have some situations with nucleo-stabilized GEN 1 particles in the chemistry [consider stable neutrons within nuclei vs. a 10.2 minute half-life when flying free]), but I seriously doubt that _we'd_ survive such a transition. Consider: in the real world, GEN 2 “molecules” (e.g.: Λ(1405)) live for picoseconds, if at all (mesonic “molecules” have yet to be observed with certainty); given this, how long do you suppose a typically stable modern GEN 1 baryonic “molecule” (e.g.: p+, n0) might survive in a GEN 0 scenario before cooling down to the lower rest mass ground state?

If the above paragraph held true, then you'd need quite a few more GEN 0 atoms to build an object of the same mass as we'd expect in a mostly GEN 1 universe, but if the orbitals were indeed far closer, then you might not see a huge change in volume (I'd love to pursue that idea, but refuse to go that far, even assuming that I have the math at my disposal [which is unlikely]). I'm not even going to guess at what planets and stars might be like there (if such things could exist in this situation), nor what sorts of new objects might show up.

But could they form nuclear structures? Right now, in a GEN 1 world, we know that our nucleons obviously can. There's sufficient binding energy available to them, and sufficient Pauli degeneracy pressure preventing a condensate. We also don't see nucleonic resonances [Δ] or any of the other hadrons (notably those {11s, 1ss, sss} with mean lifetimes of ~10-10-10-11 s and approximately nucleonic masses) forming stable nuclei (hypothetical systems aside). Maybe it's simply a watershed maximum that GEN 1 falls beneath (and that GEN 0 presumably would as well [anyone care to model some GEN 1.5 masses right on the border of stability/instability?]); maybe it's simply a question of whatever the lowest generation is (in which case, maybe no more GEN 1, but no problem for GEN 0). I really have no idea. For a story or game idea, I'd say sure, let's assume so, it sounds like fun; for an actual answer, I'd need a lot more math and data to even conjecture on it.

If we were to try to stick a few together, then they'd be much lighter, and their masses would almost certainly have much higher ratios of binding energy to constituent valence quarks' rest mass (run the numbers for hadrons: they show exactly that pattern already, so this is a _seemingly_ reasonable extrapolation for GEN 0 composites [were they to exist]; I don't have the chart that I made c2000-c2005, so I ran a new one with the 2018 PDG quark masses and a quick reference to Wikipedia's baryon masses [since the data needn't be particularly accurate], and it's a fairly steady trend (especially if you ignore Λ in favor of Σ) for J _P_ = 1/2 [3/2 too, though that's beside the point here]: qud ~99% EB , 80s-90s for uus/uds/dds [and sss, where J _P_ = 3/2], mid to upper 40s for qqc [sharp drop to ~30 at qcc], etc. – though t quarks' decay precludes hadronization, so I can't say that those would have low percentages of binding energy out their total masses). If we extrapolated that backward, then the trend would indicate p+0 = u0u0d0 and n00 = u0d0d0 as having binding energies distinctly above 99% of the total masses (consider GEN 2 equivalents: Ω+CC [scc :: p+] at ~29% and Ω0C [ssc :: n0] at ~46%).

You've probably noticed that I'm sidestepping the question of gluon exchange within N0 and of π0 between them. I don't think that I can really address the details any better than to guess blindly. Below 0.8 fm and GEN 1 is looking at gluon exchange, ~1.7-2.5 fm and it's pions; extending this to GEN 0 begs the question of N0 size and internucleon distance (and of gluons' force carrying profile, though we're assuming that this isn't changed).

####  GEN 0 nuclei and chemistry **Contents ▲**

I'm guessing that N0 would move around within such GEN 0 atomic nuclei more rapidly than our nucleons do (lower masses and possibly less-dense mass:volume [rather than simply center-oriented] packing between nucleons [e.g.: gold nuclei display [~20% slower quarks](http://news.mit.edu/2019/quark-speed-proton-neutron-pairs-0220) (in a sense) than those of helium]), and those are already somewhere around 0.25c. If so, then presumably they'd hit Dirac supercriticality far sooner than our GEN 1 theoretical Z ≈ 173 (i.e.: no bare nuclei permissible, due to spontaneous e± creation) – though if they were the other way around, then we'd presumably have a similarly larger periodic table to work with. Positing smaller nuclear and lepton shells would also imply greater uncertainty to N0 and e–0 momenta, and given their smaller masses this translates to a larger velocity (e.g.: simply taking GEN 0 e–0 shells to be of the same size as those of GEN 1 ~10e-10 m, shrinking only the mass of e– to that of e–0 ~3.34(-)e-34 kg, we get a velocity uncertainty of ~1.58(-)e9 m/s, hence a kinetic energy of ~4.6(+)e9 ergs ~2.598(-) KeV [ignoring relativistic corrections]... **1** which sounds great 'til you notice that this means that our little e–0 “could” be cruising along at ~5.27(-) c [mathematically, not realistically: it's just meant to indicate a complete uncertainty, not an actual speed], which means that the e–0 shells would have to be larger than our GEN 1 e– shells [to the corrected tune of ~10e-8 m] _if we choose to assume similar speeds to those of e –_ [hence maintaining fine structure constant α], though anything larger than ~5.27(-)e-10 m brings _**this example mass's** velocity uncertainty_ to sublight). The derivation is shown in the table below, though I'm leery of the Lorentzian transforms (E seems to be OK at relativistic speeds, but the others I'm not so sure of):

  
**_[open image in new tab](https://i.pinimg.com/originals/15/94/70/159470faaee716fb516f733cf2996819.png) to zoom_**

That brings us to the question of atomic stability. With the Fermi energy **_in this example_** , I'd expect a stronger tendency for n00 → p+0, shifting the center point of stability to something lower than iron and making the heavier elements still more unstable than they already are (assuming that iron and actinides and such are meaningful here – it's possible that actinides and maybe lanthanides would be above the GEN 0 island of stability, with yttrides and maybe scandides [or lighter still] taking their place as GEN 0's [rather light] “superheavy” elements). Conversely, it should take much less energy to excite an e–0 to a higher orbital, which might indicate a more chemically active system – if things aren't typically bare nuclei (though molecular plasma is possible). Easier excitation means easier ionization.

This in turn begs the question of molecular chemistry. Honestly, given their seemingly-probable respective Fermi levels **_in this example_** , I'd expect a decent chance of some cases of GEN 0+1 to exist in less-than-stellar conditions (no pun intended). If GEN 0 chemistry were _approximately_ as diverse as our GEN 1 chemistry... consider this: for as many molecules (and isomers and allotropes and interactions and...) as we have with 80-90 reasonably stable elements (isotopes aside), you'd expect a 0+1 chemistry to almost scale with these (naïve paired-ion molecule example: {802 = 6,400} → {1602 = 25,600}), hence any such 0+1 combined chemistry would [if scaling similarly] be far richer than our own (though of course, we don't exactly see a lot of GEN 2 chemistry present in our current GEN 1 world, which doesn't bode well for GEN 1 chemistry in a GEN 0 world).

Assuming that GEN 0 molecules were possible, with or without a GEN 1 admixture, I'd expect that they'd dissociate more easily than ours do. Just a hunch that I haven't really thought through at all (which I really should do, since I'm commenting on the thought), and it stems from the Fermi energy: if GEN 0 atoms were to ionize more easily than ours do, then perhaps GEN 0 molecules would as well. That might not matter if the background radiation were sufficiently low, but in this scenario I suppose that it's probably too high to permit molecular bonds (except _maybe_ if the atoms were of sufficiently high Z and one were sufficiently stripped to bond to another's outermost e–0 shell?). If they could, then I imagine that the binding energies available should be rather weak (note to self: **_how weak, exactly – or would they instead be fairly strong?_** ), hence lower material strengths and melting/etc. points.

That makes me wonder though (mostly in a pulp sense): let's say that you had life in each case - people from a GEN 1 universe meet people from a GEN 0 universe. “How” is assumed not to affect things for this question. If whatever means keeps them both stable doesn't also directly affect anything else, such as their physical durability, biochemistry etc., then might one expect significant differences (à la Superman, or Buck Rogers's [TV] Varek) from the nature of the generational molecules? For that matter, the biochemistry would probably be a problem for sharing food: could one really expect H2O to be the same for GEN 0 as GEN 1 for example (I mean, would you expect to be able to use GEN 2 water yourself - that is: normal “everyday” [GEN 1] [di-]deuterium oxide [di-tritium/etc., not so great an idea due to neutron overabundance] should be OK, but [if somehow able] could you trust a glass of [GEN 2] di-Ω+CC oxide)?

####  GEN 0 _terrestrial_ conditions **Contents ▲**

Given Earth's size remaining a constant, but assuming ~1/9 of the mass (for reasoning, see next subsection on stellar fusion), our surface gravity would be ~0.11(+) g; this translates to ~1.08(+)m/s2 of acceleration.

I'm not even going to take a stab at the atmosphere. A lower surface gravity on its own means less air retention; lighter air molecules means that they'd be more easily boiled off, but we're also looking at much less energetic daylight. How much air a GEN 0 Earth might be able to retain (whether after miraculously surviving a phase transition or as a result of natural planetary evolution in a GEN 0 universe) is too “iffy” for me. This means that I can't really look at heat retention or air pressure at all, much less weather, ocean currents, plate tectonics, etc..

If we consider solely the question of life forms... I'm still stuck with not knowing how to work out anything like a decent guess for molecular bond strengths (driving the strength of materials for bones, for example). As a first-order approximation, I'll say that a given life form would require less work to support itself against this gravity, hence (ignoring all other considerations) could afford to be much heavier for the same metabolic cost.

####  GEN 0 stellar fusion **Contents ▲**

I'm not about to do this in depth, but it might be fun to look at the fusion of GEN 0 nuclei here, to see what we might expect from a large gravitational mass. To do that, even if we're just playing with foo-numbers, we'd need to know just how much the nuclei weigh (assuming that we're not doing a solid workup from wave functions [that's beyond my math, sorry]). I'll take a stab at it, based upon q0 masses and extrapolating their approximate binding energies from the percentages of the higher generation hadrons' percentages (in order to find the expected p+0 and n00 masses, and guess at possible H0 / He0 / etc. masses), but nuclear physics isn't my forte (insofar as I can claim anything to be), so this will be on even shakier ground than the rest has been so far. For the moment, I'll set aside the question of whether it _could_ proceed through a series of resonance peaks (e.g.: 1H + 1H → 2H, + 1H → 3He, + 3He → 4He [each interaction plus side products]) and unlikely events (e.g.: triple alpha), and simply assume that it's possible for large masses to at least gravitate together. Maybe nuclear fusion (or some other mechanism with equivalent results, as long as we're changing physics in the first place) would or could be possible with GEN 0 nuclei, and I'd love to see that, but even if not, the gravitating masses (if large enough) presumably _would_ radiate blackbody at the least. If these “stars” couldn't fusion-ignite, then the infrared outpouring might still drive ecological cycles, but I don't know if mass contraction alone could spit out enough energy to shed visible light at all. (It might be a simple and obvious answer either way, or difficult, or the whole question is utterly inane, but I'm not feeling the draw to investigate it right at this moment.)

Given that the rest of this write-up is all fluff for a toy-model, let's just go to the hilt here. We have approximate percentages for binding energy, so we can find the quark-mass complement: {1 - 0.3611... = 0.6388...} * {1 - 0.9888... = 0.0111...} = 0.0071..., giving us N0 that are ~99.29(-)% binding energy and ~0.71(+)% valence quark mass. We already know the GEN 0 quark-masses **_for this example_** , so p+0 = u0u0d0 ~0.49(+) MeV (plus binding energy) and n00 = u0d0d0 ~0.98(+) MeV (plus binding energy). From these we find the total masses to be p+0 = u0u0d0 ~69.1071(-) MeV and n00 = u0d0d0 ~137.8102(-) MeV. For simplicity, we'll consider only one typical example: 2 11p+0 \+ 2 10n00 = 4.53346 * 10-12 J of nuclear binding energy, [following Khan Academy's lead](https://www.khanacademy.org/science/physics/quantum-physics/in-in-nuclei/v/mass-defect-and-binding-energy). I'd like to run the GEN 0 equivalent of 63Li + 10n0 = 42He + 31H + 4.7 MeV, or 21H (~1 MeV/N) + 31H = 42He (~7 MeV/N) + 10n0 \+ 17.6 MeV, and maybe another one or two, but I'll leave that as an exercise for the reader (you can find a few common examples at [Wikipedia's article on nuclear fusion](https://en.wikipedia.org/wiki/Nuclear_fusion#Criteria_and_candidates_for_terrestrial_reactions)).

42He0 _nucleus_ = 2 11p+0 \+ 2 11n00

11p+0 = 0.0741895(+) AMU each  
* 2 = 0.148379(+) AMU of 42He0's total mass  
10n00 = 0.147945(+) AMU each  
* 2 = 0.295891(-) AMU of 42He0's total mass  
42He0 = 0.148379(+) + 0.295891(-)  
= 0.44427(-) AMU

42He0 _nucleus_ = 0.44427(-) AMU **_predicted mass_**  
mass defect in _GEN 1_ 42He is ~1/132.729517(+) of the total mass  
if ~same%, then 42He0 **_mass defect_** ~0.003347(+) AMU  
& total ~0.440922(+) AMU **_actual mass_**

E0 = m0c2 (J = kg * m2/s2); 1 AMU = 1.66054e-27 kg  
m0 = 0.003347(+) AMU **_mass defect_**  
* 1.66054 * 10-27 kg/AMU  
= 5.558127(-) * 10-30 kg **_mass defect_**  
c2 = 8.987552(-) * 1016  
⸫ E0 = 4.995395(+) * 10-13 J of nuclear binding energy  
_where E 0 indicates energy of **rest mass** , not some kind of magically different GEN 0 energy_

The bottom line is that, unsurprisingly, with the n00 & p+0 weighing 1/13.58(-) & 1/6.82(-) of the GEN 1s, 4He0's binding energy comes out **_in this mock up_** as 1/9.08(-) of normal 4He. In other words, about 11% of normal energy production, if GEN 0 stars could exist (I presume that this wouldn't necessarily be the same exact percentage for other fusion equations, but it shows the basic process to derive other equations' equivalents for GEN 0). This is just the barest treatment of fusion. It doesn't even address the equation of state for GEN 0 degeneracy pressures.

If we were to assume some universe that worked as described so far (i.e.: GEN 0 quarks and leptons of some masses distinctly less than GEN 1's, and consequent results, but no other changes [such as other GENs' masses, any force's strength, universe's physical dimensions, etc.] that aren't causally required [unless we model them as unchanged by fiat]), then a gravitating body of _a given volume would contain much less mass there_ than a body of the same size would be here (rewording that, since sometimes the choice of wording can muddle or clarify things: a body of _a given mass would be larger in volume there_ than a body of the same mass would be here).

####  GEN 0 quark stars **Contents ▲**

Everybody loves white dwarfs and neutron stars, right? These days, it's a popular enough topic that you've likely run into articles on strange stars and nuggets of strange matter. There doesn't seem to be much hope for quark stars of c, b, or t, but s is at least still a possibility.

This is an extrapolation drawn from material in _The Anthropic Cosmological Principle_ , John D. Barrow & Frank J. Tipler, Oxford UP; New York, 1986. I had looked at it originally as a general question of quark stars in the late '80s or early '90s, only to find in the mid- to late-'90s that I had been scooped (Ed Witten had done a really in-depth paper on it in '84 for Phys. Rev. D [I'd swear that it's not the “[Cosmic separation of phases](https://drive.google.com/file/d/0Bxi3NrtyyNTaOGdqQ1RUVEpXZm8/view?usp=sharing)” paper, but I must be wrong – I have that and [a good Zel'dovich](https://drive.google.com/file/d/0Bxi3NrtyyNTaN1ItRjdZT3NxRW8/view?usp=sharing), if you're interested in them] – and it later turned out that he too had been scooped at least once in the '70s by a Chinese group, though I can't remember their names just now). The funny thing is that I have some old URLs on my later quark star research, and they all come up unreachable these days (or excluded in the case of LANL on Wayback).

That aside though, you can use it as a jumping-off point for the question of quark stars in a hypothetical GEN 0 situation.

Below, I've copy-and-pasted some of my [incomplete] notes from a 2005 .doc version – but have only quickly skimmed them for format; I have yet to update them to a GEN 0 context, flesh them out, and check for typos/errata.

> Note:  
>  r0 = distance of closest approach, classically; dq same, for quarks  
>  α = fine structure constant (2002 CODATA value ≈ 7.297 352 568 (24) x 10-3)  
>  (2018 CODATA value ≈ 7.297 352 56 **9 3(11)** x 10-3)  
>  αG = binding energy, gravitational.(2002 CODATA value ≈ 6.6742±0.001 x 10-11 m3 s-2 kg-1)  
>  (2018 CODATA value ≈ 6.674 **30(15)** x 10-11 m3 s-2 kg-1)  
>  αS = binding energy, strong force

> Relativistic T° for particlesx (T ≥ mx): 1 / d2me-  
>  where d is mean distance between particles [as used in source material]

> Non-relativistic:  
>  given e- degeneracy pressure ≈ _p_ 2me-–1 ≈ dn2me-–1  
>  where _p_ is momentum;  
>  given n0 degeneracy pressure ≈ r0-2mn0-1  
>  ⇒IMP q degeneracy pressure ≈ dq2mq-1 **?**
> 
> Relativistic stellar e- degeneracy pressure ≈ d(e-)-1
> 
> White dwarf:  
>  MWD ≈ αG-3/2MN  
>  RWD ≈ αG-1/2me--1 :: 1/(αG1/2me-)  
>  PWD ≈ mNme-3 ≈ 109gm cm-3
> 
> Neutron star:  
>  MNS = ...  
>  RNS ≈ r0N1/2 ≈ 10 (M/M0)1/3gm :: 1/(αG1/2mN)  
>  ⇒IMP RQS ≈ 1/(αSq1/2mq) **?**  
>  where αSq is the strong force coupling of a quark;  
>  PNS ≈ mN4(M/M0)2gm cm-3 [for P ≱ mN4]

> **Equilibrium requirements**
> 
> Neutron star 
> 
> N/r02mN ≈ GM2/R  
>  where N = MmN-1 = number of nucleons  
>  r0 = N-1/3R = radius for neutron degeneracy
> 
> If the same holds true for white dwarfs, then:
> 
> #e-/d2me- ≈ GM2/R
> 
> which would imply:
> 
> #q/dq2mq ≈ GM2/R  
>  in which Mmq-1 = #q (number of quarks [insofar as this is at all meaningful])

> If mean internucleon separation [p. 363, note 61]
> 
> r0 = d ≈ 2αSmN-1
> 
> then presumably
> 
> r0(q) = dq ≈ 2αSmq-1 **?**
> 
> (Strong) binding energy of quark
> 
> αSqm ≈ [mN-(mu+2md)]/3 ≈ [0.940-(0.004+0.16)]/3 ≈ 0.258(6̅) GeV/c2 **?**

> mn0 = 940 GeV/c2, dian0 ≈ (from 10-15 to 10-13 m)  
>  ⸫ d2-2 ≈ 1030
> 
> Mean interquark separation within neutron ≈ 0.520 mq-1 GeV/c2 ≈ 9.45 GeV/c2  
>  Mean mass of (2d + 1u) ≈ 0.054(6̅) GeV/c2  
>  ⸫ (degeneracy pressure ≈ d2-2mq-1)  
>  ⊃ (degeneracy pressure ≈ 9.45-2 * 0.055-1 GeV/c2) ≈ 0.205… GeV/c2

> If
> 
> #q/dq2mq ≈ GM2/R  
>  in which Mmq-1 = #q
> 
> Then (assuming up and down quarks only, for now)
> 
> (M★ ≈ 1031N)  
>  ⊃ (M★ ≈ 3*1031q)  
>  ⸫ (#q/dq2mq) ≈ ([3*1031]/[89.3*0.055])  
>    
>  6.11(-)*1030  
>  ≈ GM2/R  
>  where r0 ≈ 9.45, mq ≈ 0.55 GeV/c2  
>  Units of meas. R ≈ f(km)?
> 
> GM2/R ≈ ([6.6726*10-8] * M[in gm]2) / R(in km **?** )  
>  108 to 1014 (gm?) / (≱ 10 km)  
>  Here M is M★, but in what unit of measurement? (Not sols, surely?)

> **Ratio of sizes:**
> 
> q★ **:** N★  
>  = RNS/RqS  
>  ≈ mN/mq  
>  ≈ 17.1

> Must compare degen. pres. on e-, n0, & q:
> 
> e- ≈ 1/(d2me-); d ≈ 2αEMme--1  
>  n0 ≈ 1/(d2mn0); d ≈ 2αSmn0-1  
>  q ≈ 1/(d2mq); d ≈ 2αSmq-1 **?**

####  GEN 0 _solar_ evolution **Contents ▲**

Assuming that Sol's mass were dropped to ~0.11(+) M⊙ (i.e.: within the red dwarf range, toward the lower end; a little less massive than Proxima Centauri), and that the size and pressure remained the same (here we're assuming a balance of forces) – and that it weren't to simply explode outright (though maybe asking this of a universe that began with GEN 0 particles and stars is more reasonable than picturing anything remaining physically intact after such a phase transition) – then it might look there much like our stars of that same mass (~0.16 radius, ~3*10-3 luminosity) here: ~2,900 K (vs. Sol's ~6,000 K), mostly infrared (visually appearing to be something in a [light pumpkin color](https://en.wikipedia.org/wiki/Color_temperature)).

Since we're assuming that the only change here is the energy output, not the size, it would presumably have a luminosity of L = R⊙2 * T⊙4 = 12 * (~2,900/6,000)4 = ~0.05(+) L⊙ (hence appearing to be as bright there at 1 AU as Sol would be here at ~4.28(+) AU [hence <5.46% as bright]: we receive ~120,000 lux under direct noonday sunlight here; if our atmosphere there had the same effects as it has here, then we would instead receive ~6,549(-) lux there [i.e.: more than 3x that of an overcast day, less than 1/3 that of shade under a clear sky]).

If our red dwarfs' fully convective model held for the same mass range there, then it should maintain its luminosity and main sequence status for several trillion years (i.e.: it would then have ~1,000x its current life expectancy).

####  GEN 0 element distribution **Contents ▲**

Assuming that no great differences were to obtain, then we might expect nucleosynthesis to follow a pattern similar to what seems to have been the case for us. Starting with hadronization and moving along to fusion (p-process), we see helium, lithium, beryllium, etc. and various isotopes thereof (r-process and s-process). Wait around for a few stellar generations of novae/supernovae to populate the heavier elements such as iron, uranium, etc.. Maybe throw in natural decay products, or other possible cosmogenic processes (cosmic rays, neutron stars).

The results should end up with a distribution curve of how much of each element you have on hand.

Initially: pretty identical to nothing. Let things cool down a little and you have a lot of hydrogen and some percentage of helium. Given more time, you start seeing the numbers creep up in favor of heavier materials, at least until you start looking at deep time and iron stars (without going quite so far as proton decay or black hole decay products).

  
**_[open image](https://i2.wp.com/www.astronoo.com/images/elements/elements-abundance.jpg) (from [Astronoo](http://www.astronoo.com/en/articles/abundance-of-the-elements.html)) to zoom_**

If a universe had _begun_ with a GEN 0 situation (inasmuch as one might say that ours “began” with a GEN 1 situation), and there were some inherent issue such that any resulting periodic table just weren't the same (lighter cutoff of stability as conjectured, though a heavier cutoff would presumably show some quirks too), then some GEN 0 astrophysicist might look to the skies and calculate percentages and find a happy agreement between prediction and observation.

On the other hand, if a GEN 0 universe were to arise from the transformation of an extant GEN 1 universe, then that GEN 0 astrophysicist might be in for a real head-scratcher: their universe looks to be a certain age (though their stars' apparent lifespans might be calculated as a little shorter than our own, if there's any issue from the question of just where the elements' stability ends), but their elements' relative abundances would presumably be skewed far more in favor of heavy elements than they'd expect (that is: their heavier elements' distribution would imply a far older universe than they could reasonably account for, since any elements that used to be GEN 1 that are too heavy to be stable in GEN 0 would decay down toward still-fairly-heavy resulting nuclides [setting aside the question of the release of binding energy during the 1→0 process in the first place] – in fact, this might even lead to something like a bimodal distribution, since they presumably wouldn't simply decay in a nicely behaved spread with products favoring light elements: plenty of light elements since neither GEN 0 nor GEN 1 has any issue with those, plenty of heavy elements [or at least in far greater abundance than they'd predict] having decayed from heavier GEN 1 starting points, and not so many in the middle since neither process would yet have had much time to reach that point). Consider this: some element “n0” is the heaviest stable possible GEN 0 nucleus, and you convert GEN 1 element (n+20)1 to GEN 0; whether it splits into a two (n+20)0/2 = ([n/2]+10)0 nuclei, or one n0 \+ one n=200, or more than two nuclei of whatever masses, the most likely is simply something relatively heavy but stable plus some tiny extra bit(s)... and this means that you'd suddenly the right side of your graph to be more heavily populated than it would be by natural occurrence.

What would this mean for their particle physicists' study of hypernuclei, and maybe eventually hyperchemistry? Assuming that they could do so, then they'd soon be where we are now: finding “weird” GEN 1+ particles, studying their force interactions, deducing their properties, injecting them into “normal” GEN 0 nuclei, and wondering if they could stabilize these results for long term scientific study and technological application – and perhaps a public outcry over possible 1-star nuggets converting the planet to 1-matter. If you're curious, you can get a feel for them at _<https://slideplayer.com/slide/12510415/>_ or _<https://en.wikipedia.org/wiki/Hypernucleus>_ , but note that these both refer to hypernuclei in the usual sense of GEN 1 nuclei that contain baryons of 1-3 strange quarks and nothing heavier; here I'm referring to _any_ heavier than GEN 1 quark content (it's a misuse of the term, but the alternative is to say “heavy”, which similarly refers only to charmed quarks or heavier).  
You can also find an outline of hadrons in general in “[An illustrated periodic table of hadrons](https://archiveofourown.org/works/29512119)”.

####  Conclusion **Contents ▲**

The punchline to all of this is that simple rules can lead to utterly unexpected results (I wouldn't think that Conway's 23/3 rule would yield results that were at all interesting – clearly I'd be wrong), so you can't necessarily easily guess an outcome.

From that being wrong, I'd think that there would be all sorts of cool results from _any_ variation of 23/3. Again, I'd be wrong. (I.e.: sometimes you can double-guess badly when your first thought was right.)

Between these two lies the Goldilocks zone, twisted around like the Mandelbrot set: sometimes the hunt itself is the most fun of all (and that's what this GEN 0 write-up is about: assigning some value for fun, not necessarily a correct one, and seeing what it might lead to), and you might find a tiny tweak yielding surprisingly interesting or boring results. Whatever the values of GEN 0 particles might be if calculated by someone who knew what they were doing, the values here at least let us peek into what the results might look like if _these_ numbers were correct for any given step.

####  Addendum **Contents ▲**

For those who are really curious, the same [rather pointlessly unscientific] calculation method applied upward would have GEN 4 masses come out as follows (this b' would show up an order of magnitude sooner than our current lower limit research suggests [so... not terribly realistic], and the same issue shows up for leptons [at least two whole magnitudes too light], but at least the associated t' is safely above the current real world minimum mass limit), which leads me to wonder just how accurately I've run the numbers for our imagined GEN 0 particles.  
On the other hand, one could take this glaring difference as a crackerjack: maybe your characters ran into the same thing, and very definitely had made no mistakes in their data, model, math, nor verifications (whether in this particular example or any other). What might they have to conclude?

  
**_[open image in new tab](https://i.pinimg.com/originals/d3/be/8d/d3be8dab48d7f726678ea9d82590707d.png) to zoom_**

  
**_[open image in new tab](https://i.pinimg.com/originals/45/6d/6e/456d6e089ebac3affa0c55697eb89ed9.png) to zoom_**

Hmm... I wonder how things might look if [in the real world] instead of a symmetry break of weak and electromagnetism, we had experienced a break of electrical charge and magnetoweak, or magnetic charge and electroweak [a literal electroweak, sans magnetism, not the SU(2) x U(1) of the standard model], or even just the same break at different strengths (though this last is sometimes touched on in pulp sci-fi). For that matter, what if electromagnetism were particularly self-interacting at low orders (maybe photoballs would be hypothesized in such a world, much like glueballs today), or photons exhibited generational differences?

For more questions like these, see: “ _[The eighteen arbitrary parameters of the Standard Model in your everyday life](https://escholarship.org/uc/item/1st7n8mh)_ ” (Robert N. Cahn, 1996).

If you enjoy this stuff, but it's a bit too heavy, then I recommend “ _Black Holes and Time Warps_ ” (Kip S. Thorne, 1994) and “ _The Anthropic Cosmological Principle_ ” (Barrow & Tipler, 1986); the latter is primarily philosophical for the first third (or 2/3?), but gets to the physics in good time. There are also some really interesting (old) pieces from Scientific American, “ _Particles and Forces: At the Heart of Matter_ ” (1990) and “ _Particle Physics in the Cosmos_ ” (1989), which go for about $25 each on Amazon – though I imagine that there's more-up-to-date material out there by now. For more-immediately accessible reading, poke around at <http://hyperphysics.phy-astr.gsu.edu/hbase/index.html>.

On a more whimsical note, you might like the magmatter write-up at Orion's Arm, or their fascinating article on neutron star vortex biology:  
<https://orionsarm.com/eg-article/53961a52bb97a>  
<https://orionsarm.com/eg-article/46709d53449d2>

If this material is too light and fluffy for your level, then I recommend <https://arxiv.org/>. Really good material there, some of it being fairly standard and some rather bleeding edge. You won't be disappointed (though sometimes you'll need your Google Fu in order to find the more rare items elsewhere).

You might also consider <http://vixra.org/>; it has a bit of disrepute to it, but that doesn't necessarily make a given paper wrong – and regardless of veracity or lack thereof, that doesn't necessarily mean that something isn't an interesting read, or might not spark a perfectly valid line of reasoning (or game / fiction ideas).

**O ~~~ O**

**Author's Note:**

>  **1** Heisenberg uncertainty:
> 
> σxσp ≥ h/4π
> 
> σp = mσv = ~6.62e-34 J*s / 4 π ~1e-10 m = ~5.27(+)e-25 kg*m/s
> 
> σv = σp/m = ~5.27(+)e25 kg*m/s / ~3.34(-)e-34 kg = ~1.58(-)e9 m/s … i.e.: ~5.26(-) c (stems from small σx)
> 
> KE _C_ = 0.5 mv2 = 0.5 * ~3.34(-)e-34 kg * (~4.98(+)e19 kg*m/s)2 = 4.16(+)e-16 J = ~4.16(+)e-9 ergs = ~2.6(-)e3 eV
> 
> σx = ~2.73(-)e-8 m would give σp = ~1.93(+) kg*m/s ⸫ σv = ~5782785(-) m/s ⸫ KE _C_ = ~5.58(+)e-21 J = ~0.03 eV
> 
> (And if you'd like to be able to highlight your text as I did in this footnote -- or change font color, size, fonts, etc. -- here's my tutorial as a starting point: “[Fonts, and colors, and work skins, oh my!](https://archiveofourown.org/works/28934610)”)


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